Near the beginning. . . there was Quark-Gluon Plasma Department of Physics, The , Tucson

BNL Physics Colloquium, January 21, 2014

Journey in time through the universe from a visit to the quark-gluon plasma era: Matter surrounding us arose from the primordial phase of matter, Quark-Gluon Plasma (QGP). QGP was omni-present up to when the Universe was 13 microsec- onds old, just the time it takes for heavy ions to travel around the BNL-RHIC ring. As the universe expands and cools QGP hadronizes, forming abundant matter and antimatter. Only a nano-fraction surplus of nuclear matter sur- vives annihilation process. A dense electron-positron-photon-neutrino plasma remains. The description of neutrino chemical and kinetic freeze-out dynam- ics requires use of the methods we developed in study of hadron freeze-out in QGP . Electrons and positrons begin to annihilate nearly at the same time when neutrinos decouple. Electron-positron-annihilation process lasts through the big-bang nucleo-synthesis (BBN) period. In the background of free streaming dark matter and neutrino fluids the visible matter evolves till ion-electron recombination completes, and the Universe becomes transparent to free-steaming light we observe as the cosmic microwave background.

1 Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 2 The next hour is about • In depth look why we do relativistic heavy ion physics and: • Applying this to the understanding of the Quark-Hadron Universe • Applying non-equilibrium methods developed in RHI to other time epochs

Past decade primary contributors: (former) students were (αβ’ic): Jeremey Birrell, Michael Fromerth, Inga Kuznetsowa, Lance Labun Michal Petran, Giorgio Torrieri

supported by the U.S. Department of Energy, grant DE-FG03-95ER41318. Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 3 Outline • The intellectual and historical pillars of RHI-QGP physics - extended version • The beginning: Experimental HI Program • The beginning: Introduction to cosmology and survey of three epochs of cosmic evolution: QGP, ν-decoupling – BBN, Ion-electron Recombination • Differences to QGP in laboratory: time scale, baryon content, size scale TIME PERMITTING • Quark-lepton Chemistry • Universe with mixed quark-hadron phase • Hadron Universe emerges Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 4

Intellectual Pillars of QGP/RHI Collisions Research Program

RECREATE THE EARLY UNIVERSE IN LABORATORY: Recreate and understand the high energy density conditions prevailing in the Universe when matter formed from elementary degrees of freedom (quarks, glu- ons) at about 13 µs after . QGP-Universe hadronization led to a nearly matter-antimatter symmetric state, the later ensuing matter-antimatter annihilation leaves behind as our world the tiny 10−10 matter asymmetry. There is no understanding of when and how this asymmetry arises.

INVESTIGATE STRUCTURED QUANTUM (Einsteins 1920+ Aether) The vacuum state determines prevailing fundamental laws of nature. Demonstrate by changing the vacuum to the color conductive deconfined ground state.

STUDY ORIGIN OF THE INERTIA OF MATTER The confining vacuum state is the origin of 95% of inertial mass, the Higgs mechanism applies to the remaining few%. We want to: i) confirm the new paradigm; ii) explore the connection between charge and inertia; iii) understand how when we ‘melt’ the vacuum structure setting quarks free the energy locked in the mass of nucleons is transformed.

SEARCH FOR THE ORIGIN AND MEANING OF FLAVOR Normal matter made of first flavor family (u, d, e, [νe]). Strangeness and charm [at LHC] rich quark-gluon plasma the sole laboratory environment filled with 2nd family quark matter (s, c)– arguable the only experimental environment where we could study matter made of 2nd flavor family. Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 5 The Riddle of Three Generations of Matter

In QGP we excite a large number of particles of Generation II – this should present an opportunity to explore foundation of flavor physics. Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 6

Vacuum Structure: Origin of Physics Laws Relativistically Invariant Aether 1920: Albert Einstein at first rejected æther as unobservable when formulating special relativity, but later changed his position. “It would have been more correct if I had limited myself, in my earlier publications, to empha- sizing only the non-existence of an æther velocity, instead of arguing the total non-existence of the æther, for I can see that with the word æther we say nothing else than that space has to be viewed as a carrier of physical qualities.” letter to H.A. Lorentz of November 15, 1919 In a lecture published in Berlin by Julius Springer, in May 1920, presentation at Reichs-Universit¨atzu Leiden, addressing H. Lorentz delayed till 27 October 1920 by visa problems, also in Einstein collected works: In conclusions: . . . space is endowed with physical qual- ities; in this sense, therefore, there exists an æther. According to the general theory of relativity space without æther is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. But this æther may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time.The idea of motion may not be applied to it.

The QGP created in laboratory is a ponderable fragment of the early Universe: is this possible? Berndt Muller and I worked on this in early ’70s: Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 7 Formation of Local Domain of Charged Vacuum Pair production across (nearly) constant field fills the ‘dived’ states available in the localized domain. ‘Positrons’ are emitted. Hence a localized charge density builds up in the vacuum reducing the field strength - back reaction. Charged vacuum ground state ob- servable by positron emission.

Rate W per unit time and volume of positron (pair) production in presence of a strong electric field |E~ | first made explicit by J. Schwinger, PRD82, 664 (1950). c (eE)2 X∞ 1 W = ImL = e−πEs/E,E = m2c3/e~ eff 8π3 (~c)4 n2 s e n=1

What is special about Es? For E → Es vacuum unstable, pair production very rapid, field cannot be maintained. Quantum physics allows local changes in the aether Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 8 Strong Fields and Charged Vacuum Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 9 The Structured Vacuum 1985 booklet

We constructed interdisciplinary rela- tion between Strong Fields–Casimir–High T–Deconfinement–Higgs vacuum Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 10 Relativistic Heavy Ions - the Beginning

I was told that I am too young without track record and was denied access to the ‘Bear Mountain’ meeting set-up to advance RHI program. Of all participants as far as I can see only TD Lee had published on vacuum structure at that time. No wonder the US community kept on 10y long discussion of what and how to do. Phase transition at the “Quark Matter” meeting in September 1983 at BNL! This happened since: Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 11

RHI experiments needed a signature of QGP and deconfinement

⇐= JR & , preprint CERN-TH-2969, Oct.1980 From Quark Matter to Hadron gas in“Statistical Mechanics of Quarks and Hadrons”, H.Satz, ed.,Elsev. 1981. s/¯ q¯ → K+/π+, → Λ/p¯ are proposed as signatures of chemically equilibrated deconfined QGP phase, near matter- antimatter symmetry discussed. As of 1981 kinetic strangeness produc- tion by gluon fusion in QGP, PRL with Berndt Muller submitted in Decem- ber 1981. Details on multistrange an- tibaryons appeared in Phys. Reports Fall 1982. Hadronization developed 1982-5, pubs with Peter Koch, PhD thesis ⇒ 1985/6, Phys. Reports. Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 12

In QGP strangeness production by gluon fusion

I shared an office at CERN 1977-79 with Brian Combridge who studied the mechanisms of perturbative QCD charm production, showing glue based process dominated – Berndt Muller and I used Brian’s cross sections to compute the thermal invariant rates and prove that equilibration of strangeness in QGP is in experimental reach. This creates the need to introduce approach to chemical equilibrium yield in QGP. Dependent on aspect ratio of quark densities in QGP and streaming hadrons this can result in just about any level of strange hadron abundance in the final hadron count. Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 13

RHI Strangeness signature of QGP and Deconfinement Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 14 Move forward decades of RHI work ⇒ quark-hadron Universe Today we are ready to explore setting the beginning at Electro-Weak vacuum freeze: • The expansion of the QGP Universe, • The conversion of Quark Universe into hadrons, • The dynamics of matter-antimatter annihilation and hadron disappearance in the range 300 < T < 3 MeV and, • The emergence of particle content as seen today. • Connecting the evolution of plasma Universe towards neutrino decoupling to era of disappearance of e+e−-pairs and BBN For most part we journey back to the quark-hadron Universe Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 15

Introduction to Cosmological Evolution I Standard cosmological Friedmann-Lemaˆıtre-Robertson-Walker (FLRW) model is based on space-time metric · ¸ dr2 ds2 = c2dt2 − a2(t) + r2(dθ2 + sin2 θφ2 1 − kr2 The space has (expanding) flat-sheet properties for the experimentally preferred value k = 0. The Einstein equations are µ ¶ R Gµν = Rµν − − Λ gµν = 8πG T µν,R = g Rµν,T µ = diag(ε, −P, −P, −P ). 2 N µν ν

It is common to absorb Λ into the energy and pressure, εΛ = Λ/8πGN ,PΛ = Λ/8πGN and we implicitly consider this done from now on. There are two dynamically independent Friedmann equations µ ¶ 8πG a˙ 2 + k k 4πG a¨ N ε = = H2 1 + , N (ε + 3P ) = − = qH2 3 a2 a˙ 2 3 a where Universe dynamics is characterized by two quantities, the Hubble param- eter H(t), a strongly time dependent quantity on cosmological time scales, and the acceleration parameter q(t), a highly useful diagnostic of Universe behavior a˙ a¨ aa¨ ≡ H(t), ⇒ = −qH2; q ≡ − , ⇒ H˙ = −H2(1 + q). a a a˙ 2 Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 16

Introduction to Cosmological Evolution II Solving both Friedmann equations for 8πG/3 and equating we find a constraint for the accelera- tion parameter: µ ¶ µ ¶ 1 P k q = 1 + 3 1 + 2 ε a˙ 2 Restricting to case k = 0: Radiative Universe 3P = ε → q ' 1; In the early Universe almost always radiation dominance Matter dominated Universe P/ε << 1 → q ' 1/2; Dark energy dominated Universe P = −ε → q = −1.

The third independent equation arises directly from divergence freedom of the homogeneous energy momentum tensor of matter ε˙ a˙ T µν|| = 0 ⇒ − = 3 = 3H, ν ε + P a same condition follows from local conservation of entropy, dE +P dV = T dS = 0, dE = d(εdV ), dV = d(a3) and divergence freedom of the left hand side of Einstein equations.

The composition of the Universe at any given epoch defines prevailing equation of state relation 2 of P, ε. For k = 0 the energy density must be ‘critical’, εcr ≡ 3H /8πGN . Given the initial condi- tions today we integrate back in time. We assume ‘Planck’ fit to present day conditions defining the equations of state 69% dark energy, 26% dark matter, 4.8% Baryons.

Tacit ‘natural’ assumptions: Dark matter mass scale e.g. M = 1 TeV is outside energy range of our study, dark matter decay and/or annihilation is mostly complete before QGP hadronization and does not impact the inventory of visible matter. Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 17

From the present day back beyond ion recombination: the almost ‘visible universe’ T H −1 [eV] q −6 [s ] 1 + z 7 3 10 10 10 Radiation dominated −7 1 10 −8 6 2 10 10 10 0.8 −9 10 5 0.6 −10 1 10 10 10 Matter dominated 0.4 −11 10 4 0 −12 10 10 0.2 10 −13 10 0 3 −1 −14 10 10 10 Dark Energy −0.2 −15 10 2 −2 dominated 10 Tγ −16 10 −0.4 10 T −17 H ν −0.6 10 1 −3 10 10 q −18 1 + z −0.8 10 −19 0 10 10 −1 0 1 2 3 4 5 6 7 8 9 10 −1 0 1 2 3 4 5 6 7 8 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 t t [yr] trecomb treion t [yr] recomb treion Temperature T , deceleration parameter q; Hubble parameter H, redshift z + 1.

NOTE: this is in essence reproduction of the ‘Planck’ study of the connection of cosmic microwave background fluctuations, SN-standard candles which we employed. Started with Planck value Hnow Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 18 Composition of the ‘present day’ Universe

0 10

−1 10

−2 10

−3 10 Dark Energy Dark Matter Baryons

−4 γ 10

Energy Density Fraction ν

−3 −2 −1 0 1 10 10 10 10 10 T [eV] Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 19

Going back from before BBN to before antimatter era: the ‘connection’ H −1 z T [MeV] q 0 [s ] 1 + 12 10 10

1 10 1 −1 10

11 −2 10 0.99 10 0 10 −3 10 0.98 10 −4 10 −1 10 10 −5 0.97 10 9 10 −2 T −6 10 γ 10 0.96 H Tν −7 10 q i f 1 + z t ti 8 tk tBBN tBBN k BBN 10 −3 −8 10 0.95 10 −3 −2 −1 0 1 2 3 4 −3 −2 −1 0 1 2 3 4 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 tf 10 t [s] t [s] BBN Temperature T , deceleration parameter q; Hubble parameter H, redshift z + 1 .

10 10

9 10

8 10 + − + − 7 10 Number of e e -pairs per baryon through BBN. e e pairs

6 10 dominates largely the number of baryons through the

5 10 BBN period, a fact which deserves more thought.

4 10

pairs per baryon 3 10 ±

e 2 10

1 10 tf ti BBN BBN 0 10 −1 0 10 10 T [MeV] Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 20 Composition of the ‘recent’ Universe

0 10

−1 10

−2 10

Dark Matter −3 10 Baryons e± γ ν −4 10 ±

Energy Density Fraction µ π±,0

−5 −4 −3 −2 −1 0 1 10 10 10 10 10 10 10 T [MeV] Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 21 A few words about neutrinos: decoupling and degrees of freedom Chemical (particle number changing reactions) decoupling at a few MeV, exact point of no concern as it happens in a very bland Universe.

Kinetic decoupling at lower T as all scattering process matter, now near begin- ning of e+e− annihilation time period.

Problem: Some of energy from e+e− can flow to neutrinos. We compare the total neutrino energy density to the energy density of a massless fermion with two degrees of freedom and standard photon reheating (all e+e− entropy flows into photons): εν Nν ≡ ³¡ ¢ ´4 . 7 2 4 1/3 120π 11 Tγ Remember: the cosmological effective number of neutrinos is distinct from the f number of neutrino flavors, Nν = 3, though the latter certainly would impact the f former should there be any doubt about the value of Nν .

After decoupling neutrino free-stream with regard to scattering but interact gravitationally and impact expansion speed of the Universe to a degree that one can see the value Nν both at BBN and at ion recombination. There is bias towards a value Nν ' 3.5. Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 22 Kinetic decoupling and degrees of freedom in detail

5 1.4

4.75

4.5 1.3

4.25 ν ν 046

4 . 1.2 /T N γ T = 3

3.75 ν 36 N .

= 3 1.1 3.5 ν Nν 62 . N Tγ/Tν 3.25 = 3 ν N 1 3 −1 0 1 10 10 10 Tk/me J. Birrell et al “Relic neutrinos: Physically consistent treatment of effective number of neutrinos and neutrino mass” PRD in press, arXiv:1212.6943 Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 23

Forward: from EW symmetric world to QGP hadronization T [MeV] q −1 5 5 H [µs ] 1 + z 10 1 10 H 15 Disappearance 1 + z 10 0.99 4 of qb, τ, qc. 10 0.98 4 Disappearance 10 3 of qt, h, Z, W 0.97 10 14 0.96 10 2 10 0.95 3 10 0.94 1 10 13 0.93 10 0 10 2 0.92 10 T Bag dark q energy 0.91 −1 10 12 0.9 10 −5 −4 −3 −2 −1 0 1 −4 −3 −2 −1 0 1 10 10 10 10 10 10 10 10 10 10 10 10 10 t [µs] t [µs] Temperature T , deceleration parameter q; Hubble parameter H, redshift z + 1.

175 B = (81 MeV)4 4 170 B = (162 MeV) B = (243 MeV)4 165 T near the QGP phase transition for several values of the

160 bag energy density.

155 [MeV]

T 150

145

140

135 10 11 12 13 14 15 16 17 t [µs] Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 24

What Controls Quark-Hadron Time Scale in the Universe? with ² + P = (4/3)(ε − B) and entropy conserving evolution in Friedmann equation: 3ε ˙2 = 128πG ε (ε − B)2,

2 Set ε = z B and t = xτU with: q q 2 τ = 3c = 25 B0 µs, B = 0.4 GeV U 32πGB B 0 fm3

leads to (z0)2 = (z2 − 1)2 . Physical solution: µ ¶ 2 t0 + t ² = B coth , x = t/τU, τU for B → 0: massless particles=radiative universe: 3 1 ² = 2 32πG (t0 + t) The QGP Universe expands as, ³ ´ s coth t0+t µ ¶ τU t0 + t H = , a = a0 sinh 2τU τU

We see that characteristic time of evolution (and phase transformation) is measured in 10’sµs. Col- lision time in laboratory is 17 orders of magnitude - case studies - QGP-Hadron Uni- shorter. Test of QGP equilibration vital to under- verse: Pressure (upper) and tempera- stand how to use lab results to characterize the ture (lower part) as function of time early Universe. Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 25

Is QGP Hadronization in the Lab the Same as in Early Universe? ] 3 LHC 0.6 RHIC62

[GeV/fm 0.5 ε

] 0.4 -3

0.3 /10 [fm σ 0.2 ] 3 0.1

P [GeV/fm 0 50 100 150 200 250 300 350 400

Npart Open Symbols: RHIC-62, Filled Symbols LHC-2.76. Analysis of data by Michal Petran et al: Phys. Rev. C 88, 034907 (2013), DOI:10.1103/PhysRevC.88.034907 . Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 26

Chemical composition and evolution of the early Universe Our Objectives: 1) Describe in quantitative terms the chemical composition of the Universe be- fore, at, and after EQUILIBRIUM hadronization near to: T ' 150 MeV t ' 30µs, including period of matter-antimatter annihilation, the residual matter and hadronic particles evolution.

2) Somewhat beyond current capability: describe the dynamics of quark-hadron phase transformation (preferably with nucleation dynamics) allowing for con- trast ratios and baryon and strangeness number distillation; opportunities for future research.

3) Describe precisely the composition of the Universe during evolution towards the condition of neutrino kinetic decoupling T ' 1 MeV t ' 3 s 4) Connect to BBN in a study of neutrino freeze-out, ee¯-plasma annihilation.

We will require input from experimental anchor points Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 27

Chemical potentials control particle abundances

p 1 f(ε = p2 + m2) = eβ(ε−µ) ± 1 Relativistic Chemistry (with particle production) • Photons in chemical equilibrium, assume the Planck distribu- tion, implying a zero photon chemical potential; i.e., µγ = 0. • Because reactions such as f + f¯ ­ 2γ are allowed, where f and f¯ are a fermion – antifermion pair, we immediately see that

µf = −µf¯ whenever chemical and thermal equilibrium have been attained.

• More generally for any reaction νiAi = 0, where νi are the reaction equation coefficients of the chemical species Ai, chemical equi- librium occurs when νiµi = 0, which follows from a minimization of the Gibbs free energy. • Weak interaction reactions assure:

µe − µνe = µµ − µνµ = µτ − µντ ≡ ∆µl, µu = µd − ∆µl, µs = µd , Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 28

• Neutrino oscillations νe ­ νµ ­ ντ imply equal chemical poten- tial:

µνe = µνµ = µντ ≡ µν, and the mixing is occurring fast in ‘dense’ early Universe matter. Remarks: 1. These considerations leave undetermined three chemical poten- tials and we choose to solve for µd, µe, and µν. We will need three experimental inputs.

2. Quark chemical potentials can be used also in the hadron phase, 0 e.g. Σ (uds) has chemical potential µΣ0 = µu + µd + µs

3. The baryochemical potential is: 1 3 3 3 µ = (µ + µ ) = (µ + µ ) = 3µ − ∆µ = 3µ − (µ − µ ). b 2 p n 2 d u d 2 l d 2 e ν Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 29

(Chemical) Conditions/constraints fixing three parameters Three chemical potentials follow solving the 3 available constraints: i. Global charge neutrality (Q = 0) is required to eliminate Coulomb energy. Local condition: X nQ ≡ Qi ni(µi,T ) = 0, i where Qi and ni are the charge and number density of species i. ii. Net lepton number equals net baryon number (L = B): often used condition in baryo-genesis: X nL − nB ≡ (Li − Bi) ni(µi,T ) = 0, i This can be easily generalized. As long as imbalance is not competing with large late photon to baryon ratio, it is hidden in slight neutrino-antineutrino asymmetry. iii. The Universe evolves adiabatically, i.e. Fixed value of entropy-per-baryon (S/B) P σ σ (µ ,T ) ≡ P i i i = 3.2 ... 4.5 × 1010 nB i Bi ni(µi,T ) Note, current value S/B = 3.5 × 1010 but results shown for older value 4.5 × 1010 See on-line Hadronization of the quark Universe Michael J. Fromerth, Johann Rafelski (Arizona U.). Nov 2002. 4 pp. e-Print: astro-ph/0211346 Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 30

TRACING µd IN THE UNIVERSE T (MeV) +0.11 700 160 100 10 Minimum µb = 0.33−0.08 eV. µb relevant at final hadron 2 µ 313.6 MeV 10 d µ (π, N) freeze-out. e µ ν 0 -5 10 10 µ phase transition d µ e µ -2 ν 10 -6 10 1 eV

(MeV) -4

µ 10 (MeV) -6 1 eV µ -7 10 10

-8 10 -8 10 0 1 2 3 4 10 10 10 10 10 10 100 t (µs) t (µs) Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 31

Mixed Phase – Case differs from RHI hadronization 2 Conserved quantum numbers (e.g. baryon and strangeness densities) of the Universe jump as one transits from QGP to Hadron Phase – ‘contrast ratio’. Thus there must be mixed hadron-quark phase and parametrize the partition function during the phase transformation as

ln Ztot = fHG ln ZHG + (1 − fHG) ln ZQGP fHG represents the fraction of total phase space occupied by the HG phase. This is true even if and when energy, entropy, pressure smooth (phase transformation rather than transition). We resolve the three constraints by using e.g. for Q = 0: h h QGP HG QGP HG Q = 0 = nQ VQGP + nQ VHG = Vtot (1 − fHG) nQ + fHG nQ where the total volume Vtot is irrelevant to the solution. Analogous expressions are used for L − B and S/B constraints. Note that fHG(t) is result of dynamics of nucleation, assumed not generated here

We assume that mixed phase exists 10 µs and that fHG changes linearly in time. Actual values will require dynamic nucleation transport theory description. Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 32

Charge and baryon number distillation

Initially at fHG = 0 all matter in QGP phase, as hadronization progresses with fHG → 1 the baryon component in hadronic gas reaches 100%.

The constraint to a charge neutral universe conserves sum-charge in both fractions. Charge in each frac- tion can be finite. SAME for baryon number and strangeness: distillation!

0.1

0.05

B A small charge separation introduces

/ n 0 Q

n a finite non-zero Coulomb potential and this amplifies the existent -0.05 baryon asymmetry. This mechanism HG QGP noticed by Witten in his 1984 paper,

-0.1 and exploited by Angela Olinto for 0 0.5 1generation of magnetic fields. fHG Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 33

MECHANISM OF HADRO-CHEMICAL EQUILIBRATION Inga Kuznetsova and JR 1002.0375, Phys. Rev. C 82, 035203 (2010) and 0803.1588, Phys.Rev. D78, 014027 (2008) The question is at which T in the expanding early Universe does the reaction π0 ↔ γ + γ ‘freeze’ out, that is the π0 decay overwhelms the production rate and the yield falls out from chemical equilibrium yield. Since π0 lifespan (8.4 10−17 s) is rather short, one is tempted to presume that the decay process dominates. However, there must be at sufficiently high density a detailed balance in the thermal bath Presence of one type of pion implies presence of π±, those can be equilibrated by the reaction: π0 + π0 ↔ π+ + π−. ρ ↔ π + π, ρ + ω ↔ N + N,¯ etc All hadrons will be present: the π0 creates the doorway. We develop kinetic theory for reactions involving three particles (two to one, one to two). We find that the expansion of the Universe is slow compared to pion equilibration, which somewhat surprisingly (for us) implies that π0 is at all times in chemical equilibrium – at sufficiently low temperatures e.g. below e.g. 1 MeV, the local density of π0 maybe too low to apply the methods of statistical physics. Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 34

16 10 16 e+e− → π+ π− 10 + − τ γ γ → π π µ 14 + − + − 10 (e e , γ γ) → µ µ 14 τ ± 10 ± π γ γ → π0 µ lifespan τ π0 π0 π0→ π+ π− 12 T/(m H) 10 12 ± π e+e− → π0 10 π lifespan

10 10 10 10

π0π0 ↔ π+π− 8 8 10 10 [as] τ

[as] 6

6 τ 10 10 γγ(e+e−) ↔ µ+µ− 4 4 10 10

2 2 10 10

0 10 0 10 −2 10 10 20 30 40 1 T [MeV] 10 T [MeV] Relaxation times for dominant reactions for pion (and muon) equilibration. At small temperatures T < 10 MeV relaxation times for µ± and π± equilibration be- comes constant and much below Universe expansion rate and τT (dotted turquoise line on right). Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 35

Hadronic Universe Hadron Densities 40 10 nuclear dens. protons neutrons 35 π0 10 − ) π 3 π+ lambdas 30 antiprotons 10 antineutrons antilambdas

25 10 atomic dens.

density (particles / cm 20 10

15 10 1 10 100 T (MeV) Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 36

Universe Lepton Densities

40 10 nuclear dens. electrons muons 35 taus 10 positrons )

3 antimuons antitaus neutrinos (total) 30 10 antineutrinos (total)

25 10 atomic dens.

density (particles / cm 20 10

15 10 1 10 100 T (MeV) Jan Rafelski, ArizonaQGP: Journey in the Universe BNL January 21,2014 , page 37

Did we find something worth continuing?

• Cosmic evolution in principle fully defined and constrained by current laboratory experiments from today back to Electro-Weak phase transition, • We understand qualitatively the QGP Universe [This is the sys- tem that lattice QCD addresses directly, RHIC indirectly], • Interesting details of cosmic evolution remain in investigation:

1. Strong local inhomogeneity at QGP hadronization 2. Strangeness present in a significant abundance in early Universe down to T = 10 MeV, potential for production of strange nuclearites 3. Period of antimatter annihilation 4. Neutrino kinetic decoupling 5. BBN in presence of dense e+e−-plasma: unsettling yet scales seperate